Fractal-Enhancement of Photon Band-Gap Cavities

Prof Hemmer


For applications such as solid-state quantum computing, ultra-sensitive chemical-biological detection, and multi-spectral quantum dot detectors, it is essential to have strong coupling between the electromagnetic field and a single atom, molecule, or quantum dot.  Ordinarily this strong coupling is achieved using high Q optical resonators.  For example, experiments with ultra-cold and trapped alkali atoms show the ability to observe single atoms and to saturate optical transitions on these atoms using only the cavity vacuum field.  For these demonstrations, ultra-low-loss bulk Fabry-Perot cavities and whispering gallery micro-sphere cavities have been used, having Q’s in excess of 105.  For solid-state systems, a much more scalable design would be an array of photon-band gap cavities.  Photon band gap (PBG) cavities have so far demonstrated Q values on the order of 1000’s, with promise of 104 or greater.  However, for demanding applications, such as ultra-sensitive chem-bio detection, a much higher Q is desired.  Currently, the best such resonators are fractal-enhanced cavities.  The key concept is to incorporate a metallic fractal pattern, having a high Q plasmon mode(s), into a conventional high Q optical cavity.  When done correctly, the Q values are multiplicative and overall Q values estimated in the range of 1010-1012 have already been observed.[i]

Figure 1: Proposed fractal enhanced photon band gap cavities.  The metallic fractal patterns will require e-beam lithography with feature sizes less than 10 nm.

 The problem with these high-Q fractal patterns is that they are created by accretion of randomly grown (via a chemical method) fractal aggregates of ~ 25 nm diameter metal balls on the surface of glass cylinders that support whispering gallery modes.  Thus, a cavity-fractal system with the desired properties is created largely by accident with no control over exact spatial location. This is not very reproducible or manufacturable.  To solve this problem, the metallic fractal patterns can be fabricated by e-beam lithography (Figure 1).  The requirement is for small diameter metal dots, separated by metal-free gaps, where the gaps are significantly less than the dot diameter (i.e. in the range of 10 nm or smaller).  This requirement pushes the state-of-the-art in e-beam lithography.  Therefore, only the highest resolution e-beam machine, as proposed here, will suffice.



[i] W. Kim, V.P. Safonov, V.M. Shalaev, and R.L. Armstrong, “Fractals in microcavities: giant coupled, multiplicative enhancement of optical response,” Phys. Rev. Lett. 82, 4811 (1999).